A nonsmooth Levenberg-Marquardt method for vertical complementarity problems
In this paper, the vertical complementarity problem is studied. The problem is reformulated as a system of nonsmooth equations \(H(x)=0\). For solving this system, the nonsmooth Levenberg-Marquardt (LM) method with double parameter adjusting strategy is presented. The method is based on the computation of an element in the B-differential of a mapping \(H\) which along with a suitable choice of the LM parameter are the critical issues in the LM method. The LM parameter is adjusted based on the norm of the vector-valued minimum function and the ratio between the current and the predicted reductions. The authors investigate the computation of at least one element in the B-differential of \(H\) as it is necessary in the implementation of the algorithm, show the global convergence, and discuss the local convergence rate of the algorithm under the local error bound condition.
scientific article; zbMATH DE number 6808526
scientific article